Existence Of Zeros For Maximal Monotone Operator With Continuous Perturbation

The theory of maximal monotone operators have been produced many research results in the field of nonlinear integral equation theory,control theory and optimization,differential equations and other fields.As a kind of maximal monotone operator,p-Laplacian operator theories have been widely applied in the field of non-newtonian mechanics,cosmic physics,fluid dynamics and population dynamics issues and many other areas.The thesis mainly studies the existence of zeros for a kind of maximal monotone operator with continuous perturbation.By introducing a conceptional of the exceptional family for maximal monotone operator with continuous perturbation,we prove that the necessary condition of existence zeros for maximal monotone operator with continuous perturbation is non-existence of the exceptional family.Next we study the existence of solutions for p—Laplacian operator equations and variational inequality.The thesis is organized as follows:In Chapter 1,we introduce the background of maximal monotone operator,p-Laplacian,and exceptional family of elements,and list some basic conceptions and lemmas which are used is this dissertation.In Chapter 2,.we transform the existence of zeros for a kind of maximal monotone oper-ator with continuous perturbation into the problem of fixed points for operator.By defining exceptional family of this problem,we prove that the necessary condition of existence zeros for maximal monotone operator with continuous disturbance is non-existence of exceptional family.Next we get some results of existence zeros for maximal monotone operator with disturbances under different conditions.In Chapter 3,p—Laplacian as a maximal monotone operator,we apply the results of chapter 2 to get the existence of solutions for the p-Laplacian operator equations with continuous perturbation.In Chapter 4,the relations between existence of zeros for maximal monotone operator and the existence of solution for variational inequality are discussed by using the techniques of testing the existence of an exceptional family.